On the study of parabolic degenerate p-biharmonic problem with memory

We explore a high-order parabolic p-biLaplace equation featuring a memory term. Employing Roth’s method, we derived an approximate solution for the semi-discretized problem in time. A series of a priori estimates were established, leading to deductions on convergence, existence, uniqueness, and qualitative outcomes within appropriate functional spaces. We introduced a comprehensive discretization approach utilizing the mixed finite element method. Finaly, we conducted a numerical experiment to confirm the convergence of the proposed scheme.